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Titolo:
Thicknesses of knots
Autore:
Diao, Y; Ernst, C; Van Rensburg, EJJ;
Indirizzi:
Univ N Carolina, Dept Math, Charlotte, NC 28223 USA Univ N Carolina Charlotte NC USA 28223 Dept Math, Charlotte, NC 28223 USA Western Kentucky Univ, Dept Math, Bowling Green, KY 42101 USA Western Kentucky Univ Bowling Green KY USA 42101 ling Green, KY 42101 USA York Univ, Dept Math & Stat, N York, ON M3J 1P3, Canada York Univ N York ON Canada M3J 1P3 ath & Stat, N York, ON M3J 1P3, Canada
Titolo Testata:
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
, volume: 126, anno: 1999,
parte:, 2
pagine: 293 - 310
SICI:
0305-0041(199903)126:<293:TOK>2.0.ZU;2-B
Fonte:
ISI
Lingua:
ENG
Soggetto:
ENERGY;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
8
Recensione:
Indirizzi per estratti:
Indirizzo: Diao, Y Univ N Carolina, Dept Math, Charlotte, NC 28223 USA Univ N Carolina Charlotte NC USA 28223 h, Charlotte, NC 28223 USA
Citazione:
Y. Diao et al., "Thicknesses of knots", MATH PROC C, 126, 1999, pp. 293-310

Abstract

In this paper we define a set of radii called thickness for simple closed curves denoted by K, which are assumed to be differentiable. These radii capture a balanced view between the geometric and the topological properties of these curves. One can think of these radii as representing the thicknessof at rope in space and of R as the core of the rope. Great care is taken to define our radii in order to gain freedom from small pieces with large curvature in the curve. Intuitively, this means that we tend to allow the surface of the ropes that represent the knots to deform into a non smooth surface. But as long as the radius of the rope is less than the thickness so defined, the surface of the rope will remain a two manifold and the rope (asa solid torus) can be deformed onto K via strong deformation retract. In this paper we explore basic properties of these thicknesses and discuss the relationship amongst them.

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Documento generato il 05/08/20 alle ore 13:09:58